## The definitions, postulates, axioms, and enunciations of the propositions of the first six, and the eleventh and twelfth books of Euclid's Elements of geometry |

### From inside the book

Page 20

Ratio

Ratio

**is a mutual relation of two magnitudes of the same kind to one another , in respect of quantity**. IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other .### What people are saying - Write a review

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The Definitions, Postulates, Axioms, and Enunciations of the Propositions of ... Euclid No preview available - 2018 |

The Definitions, Postulates, Axioms, and Enunciations of the Propositions of ... Euclid No preview available - 2015 |

### Common terms and phrases

acute angle angle contained angles equal applied bisect Book called centre circumference compounded of ratios conversely DEFINITIONS described diameter divided equal angles equal straight lines equimultiples excess exterior angle extremities fall fifth four magnitudes four straight lines fourth GEOMETRY given circle given rectilineal figure given straight line greater greater ratio half homologous sides inferred inscribed interior joins less likewise magnitude taken manifest manner mean multiple opposite parallel parallelogram passes perpendicular polygons prisms PROBLEM produced PROP proportionals PROPOSITIONS pyramids rank ratio compounded reciprocally proportional rectangle contained remaining right angles segment semicircle sides equal similar similarly described sixth solid angles solid figure contained solid parallelopiped sphere square stand straight line drawn superficies tained taken THEOREM thing third three plane angles three straight lines touch triangle triangular bases triplicate ratio unequal VIII whole whole line XVII XVIII

### Popular passages

Page 8 - IF two triangles have two sides of the one equal to two sides of the...

Page 29 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 6 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Page 14 - From this it is manifest, that if in a circle a straight line bisect another at right angles, the centre of the circle is in the line which bisects the other.

Page 23 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

Page 11 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 13 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.

Page 12 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.

Page 4 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 30 - ABC, DEF have one angle in the one equal to one angle in the other, viz. the angle BAC to the angle EDF, and the sides about...